What is the general solution for 5=5+4cos(θ) ?

The general solution for 5=5+4cos(θ) is θ= pi/2+2pin,θ=(3pi)/2+2pin

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5=5+4cos(θ)

5 = 5 + 4 cos (θ)

θ = \frac{π}{2} + 2 πn, θ = \frac{3 π}{2} + 2 πn

Degrees

θ = 9 0^{\circ} + 36 0^{\circ} n, θ = 27 0^{\circ} + 36 0^{\circ} n

Solution steps

5 = 5 + 4 cos (θ)

Switch sides

5 + 4 cos (θ) = 5

Subtract

5

from both sides

5 + 4 cos (θ) - 5 = 5 - 5

Simplify

4 cos (θ) = 0

Divide both sides by

4

4 cos (θ) = 0

Divide both sides by

4

\frac{4 cos ( θ )}{4} = \frac{0}{4}

Simplify

cos (θ) = 0

cos (θ) = 0

General solutions for

cos (θ) = 0

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

θ = \frac{π}{2} + 2 πn, θ = \frac{3 π}{2} + 2 πn

θ = \frac{π}{2} + 2 πn, θ = \frac{3 π}{2} + 2 πn

cos (θ) = - 0.47

1 + tan^{2} (x) cos (x) = sec (x)

sec (θ) = \frac{6}{2}

sin^{2} (x) + cos^{2} (x) = sin (x) csc^{2} (x)

1.5 2 = 3 cos (x)

What is the general solution for 5=5+4cos(θ) ?
The general solution for 5=5+4cos(θ) is θ= pi/2+2pin,θ=(3pi)/2+2pin